Paul P. Wang, Da Ruan, Etienne E. Kerre (Eds.) Fuzzy Logic Studies in Fuzziness and Soft Computing, Volume 215 Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail: [email protected] Further volumes of this series Vol. 207. Isabelle Guyon, Steve Gunn, can be found on our homepage: Masoud Nikravesh, Lotfi A. Zadeh (Eds.) springer.com Feature Extraction, 2006 ISBN 978-3-540-35487-1 Vol. 199. Zhong Li Vol. 208. Oscar Castillo, Patricia Melin, Fuzzy Chaotic Systems, 2006 Janusz Kacprzyk, Witold Pedrycz (Eds.) ISBN 978-3-540-33220-6 Hybrid Intelligent Systems, 2007 ISBN 978-3-540-37419-0 Vol. 200. Kai Michels, Frank Klawonn, Vol. 209. Alexander Mehler, Reinhard Rudolf Kruse, Andreas Nürnberger Köhler Fuzzy Control, 2006 Aspects of Automatic Text Analysis, 2007 ISBN 978-3-540-31765-4 ISBN 978-3-540-37520-3 Vol. 201. Cengiz Kahraman (Ed.) Vol. 210. Mike Nachtegael, Dietrich Van der Fuzzy Applications in Industrial Weken, Etienne E. Kerre, Wilfried Philips Engineering, 2006 (Eds.) ISBN 978-3-540-33516-0 Soft Computing in Image Processing, 2007 Vol. 202. Patrick Doherty, Witold ISBN 978-3-540-38232-4 Łukaszewicz, Andrzej Skowron, Andrzej Vol. 211. Alexander Gegov Szałas Complexity Management in Fuzzy Systems, Knowledge Representation Techniques: A 2007 Rough Set Approach, 2006 ISBN 978-3-540-38883-8 ISBN 978-3-540-33518-4 Vol. 212. Elisabeth Rakus-Andersson Vol. 203. Gloria Bordogna, Giuseppe Psaila Fuzzy and Rough Techniques in Medical (Eds.) Diagnosis and Medication, 2007 Flexible Databases Supporting Imprecision ISBN 978-3-540-49707-3 and Uncertainty, 2006 ISBN 978-3-540-33288-6 Vol. 213. Peter Lucas, José A. Gámez, Antonio Salmerón (Eds.) Vol. 204. Zongmin Ma (Ed.) Advances in Probabilistic Graphical Soft Computing in Ontologies and Semantic Models, 2007 Web, 2006 ISBN 978-3-540-68994-2 ISBN 978-3-540-33472-9 Vol. 214. Irina Georgescu Vol. 205. Mika Sato-Ilic, Lakhmi C. Jain Fuzzy Choice Functions, 2007 Innovations in Fuzzy Clustering, 2006 ISBN 978-3-540-68997-3 ISBN 978-3-540-34356-1 Vol. 215. Paul P. Wang, Da Ruan, Vol. 206. A. Sengupta (Ed.) Etienne E. Kerre (Eds.) Chaos, Nonlinearity, Complexity, 2006 Fuzzy Logic, 2007 ISBN 978-3-540-31756-2 ISBN 978-3-540-71257-2 Paul P. Wang Da Ruan Etienne E. Kerre (Eds.) Fuzzy Logic A Spectrum of Theoretical & Practical Issues With 108 Figures and 28 Tables Professor Dr. Paul P. Wang Professor Dr. Etienne E. Kerre Department of Electrical & Department of Applied Mathematics & Computer Engineering Computer Science Pratt School of Engineering Ghent University Duke University Krijgslaan 281 (S9), 9000 Gent Science Drive, West Campus Belgium 27708 Durham, N. C. e-mail: [email protected] USA e-mail: [email protected] Professor Dr. Da Ruan The Belgian Nuclear Research Centre (SCK·CEN) Boeretang 200, 2400 Mol Belgium e-mail: [email protected] and Department of Applied Mathematics & Computer Science Ghent University Krijgslaan 281 (S9), 9000 Gent Belgium e-mail: [email protected] Library of Congress Control Number: 2007923180 ISSN print edition: 1434-9922 ISSN electronic edition: 1860-0808 ISBN 978-3-540-71257-2 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Integra Software Services Pvt. Ltd., India Cover design: WMX Design Printed on acid-free paper SPIN: 11506386 42/3100/Integra 5 4 3 2 1 0 Contents Foreword ......................................................VII Preface ........................................................ XI List of Contributors ...........................................XIII Why Fuzzy Logic? – A Spectrum of Theoretical and Pragmatics Issues Paul P. Wang, Da Ruan, and Etienne E. Kerre ...................... 1 On Fuzzy Set Theories Ana Pradera, Enric Trillas, Sergio Guadarrama, and Eloy Renedo ..... 15 Uninorm Basics J´anos Fodor and Bernard De Baets ................................ 49 Structural Interpolation and Approximation with Fuzzy Relations: A Study in Knowledge Reuse Witold Pedrycz .................................................. 65 On Fuzzy Logic and Chaos Theory — From an Engineering Perspective Zhong Li and Xu Zhang .......................................... 79 Upper and Lower Values for the Level of Fuzziness in FCM Ibrahim Ozkan and I.B. Turksen ................................... 99 Mathematical Modeling of Natural Phenomena: A Fuzzy Logic Approach Michael Margaliot ................................................113 VI Contents Mathematical Fuzzy Logic in Modeling of Natural Language Semantics Vil´em Nov´ak ....................................................135 Analytical Theory of Fuzzy IF-THEN Rules with Compositional Rule of Inference Irina Perfilieva ..................................................173 Fuzzy Logic and Ontology-based Information Retrieval Mustapha Baziz, Mohand Boughanem, Yannick Loiseau, and Henri Prade .................................................193 Real-World Fuzzy Logic Applications in Data Mining and Information Retrieval Bernadette Bouchon-Meunier, Marcin Detyniecki, Marie-Jeanne Lesot, Christophe Marsala, and Maria Rifqi ...............................219 Gene Regulatory Network Modeling: A Data Driven Approach Yingjun Cao, Paul P. Wang, and Alade Tokuta ......................249 An Abstract Approach Toward the Evaluation of Fuzzy Rule Systems Siegfried Gottwald ................................................281 Nuclear Reactor Power Control Using State Feedback with Fuzzy Logic Jorge S. Ben´ıtez-Read, J. Humberto P´erez-Cruz and Da Ruan .........299 The Fusion of Genetic Algorithms and Fuzzy Classification for Transient Identification Enrico Zio and Piero Baraldi ......................................317 The Role of Fuzziness in Decision Making Javier Montero, Victoria L´opez and Daniel G´omez ...................337 Fuzzy Linear Bilevel Optimization: Solution Concepts, Approaches and Applications Guangquan Zhang, Jie Lu and Tharam Dillon .......................351 Fuzzy Predictive Earth Analysis Constrained by Heuristics Applied to Stratigraphic Modeling Jeffrey D. Warren, Robert V. Demicco and Louis R. Bartek ...........381 Fuzzy Logic for Modeling the Management of Technology Andr´eMa¨ısseu and Benoˆıt Ma¨ısseu ................................431 Index ..........................................................457 Foreword In order to properly characterize the content of this book, it is important to clarify first the intended meaning of its title Fuzzy Logic. This clarification is needed since the term “fuzzy logic,” as currently used in the literature, is viewed either in a narrow sense or in a broad sense. In the narrow sense, fuzzy logic is viewed as an area devoted to the formal development, in a uni- fied way, of the various logical systems of many-valued logic. It is concerned with formalizing syntactic aspects (based on the notion of proof)andsemantic aspects (based on the notion of truth) of the various logical calculi. In order to be acceptable, each of these logical calculi must be sound (provability implies truth) and complete (truth implies provability). The most representative pub- lication of fuzzy logic in this sense is, in my opinion, the classic book by Peter Hajek [1]. When the term “fuzzy logic” is viewed in the broad sense, it refers to an extensive agenda whose primary aim is to utilize the apparatus of fuzzy set theory for developing sound concepts, principles, and methods for representing and dealing with knowledge expressed by statements in natural language. Although work in fuzzy logic in the broad sense is not directly concerned with the issues that are investigated under fuzzy logic in the narrow sense, the importance of the latter is that it provides the former with solid theoretical foundations. After examining the content of this book, it is easy to conclude that its title, Fuzzy Logic, refers to fuzzy logic in the broad sense. This is consistent, by and large, with the usual meaning of the term “fuzzy logic” in the literature. Indeed, most papers and books that use the term “fuzzy logic” in their titles or in their lists of keywords are, in fact, dealing with issues of fuzzy logic in the broad sense. Literature devoted to fuzzy logic in the narrow sense, which is lately referred to as mathematical fuzzy logic or formal fuzzy logic, is only a small fraction of the overall literature on fuzzy logic, and it is primarily literature shared by a relatively small community of researchers working in this area. However, in spite of this rather small visibility of fuzzy logic in the VIII Foreword narrow sense, its importance for building foundations for fuzzy logic in